Imported object is locked to world origin
A few things you could do to fix this: 

1) set the origin of the fbx file you imported to it's own geometry. 

You can do this by going to object > transform > origin to geometry in object mode with the object selected. 

2) you can set the object to be it's own user. 

This is a fix for an error caused by linking objects from other scenes. Somehow your object might have a similar response, so setting it to have it's own user may help. 

You can do that by going to object > make single user > object. Or if it has a material or data then object > make single user > object &amp; data &amp; materials &amp; tex.